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MPL

MPL is a program for computations with iterated integrals on moduli spaces of curves of genus zero with a special focus on the computation of Feynman integrals. It is based on Maple and was written and tested with Maple 16.

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From a download page you can obtain the latest version of the program, a technical user manual and supplementary files with example applications.

Literature:

The program is introduced in the article: C. Bogner, MPL – a program for computations with iterated integrals on moduli spaces of curves of genus zero

The main algorithms behind the program are presented in: C. Bogner and F. Brown, Feynman integrals and iterated integrals on moduli spaces of curves of genus zero, Commun.Num.Theor.Phys. 09 (2015) 189-238, arXiv:1408.1862 [hep-th].

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arXiv:1807.02542by: Bogner, Christian (Humboldt U., Berlin) et al.Abstract: We consider results for the master integrals of the kite family, given in terms of ELi-functions which are power series in the nome $q$ of an elliptic curve. The analytic continuation of these results beyond the Euclidean region is reduced to the analytic continuation of the two peri […]

PoS RADCOR2017 (2018) 016by: Hahn, Thomas (Munich, Max Planck Inst.) et al.Abstract: Loopedia is a new database at loopedia.org for Feynman integrals, providing both bibliographic information as well as results made available by the community. Its bibliometry is complementary to that of Inspire or arXiv, as it allows to search for integrals by graph-theoreti […]

arXiv:1712.09215by: Bitoun, Thomas (Oxford U.) et al.Abstract: We study shift relations between Feynman integrals via the Mellin transform through parametric annihilation operators. These contain the momentum space IBP relations, which are well-known in the physics literature. Applying a result of Loeser and Sabbah, we conclude that the number of master inte […]

arXiv:1712.03532PoS RADCOR2017 (2017) 015by: Adams, Luise (Mainz U., Inst. Phys.) et al.Abstract: Differential equations are a powerful tool to tackle Feynman integrals. In this talk we discuss recent progress, where the method of differential equations has been applied to Feynman integrals which are not expressible in terms of multiple polylogarithms.

CERN-TH-2017-175CP3-17-26MAPHY-AVH-2017-07MSUHEP-17-013arXiv:1709.01266MPP-2017-173Comput.Phys.Commun. 225 (2018) 1-9by: Bogner, C. (Humboldt U., Berlin) et al.Abstract: Loopedia is a new database at loopedia.org for information on Feynman integrals, intended to provide both bibliographic information as well as results made available by the community. Its bi […]

arXiv:1705.08952Nucl.Phys. B922 (2017) 528-550by: Bogner, Christian (Humboldt U., Berlin) et al.Abstract: We study the analytic continuation of Feynman integrals from the kite family, expressed in terms of elliptic generalisations of (multiple) polylogarithms. Expressed in this way, the Feynman integrals are functions of two periods of an elliptic curve. We […]

arXiv:1607.01571J.Math.Phys. 57 (2016) 122302by: Adams, Luise (Mainz U., Inst. Phys.) et al.Abstract: We show that the Laurent series of the two-loop kite integral in $D=4-2\varepsilon$ space-time dimensions can be expressed in each order of the series expansion in terms of elliptic generalisations of (multiple) polylogarithms. Using differential equations w […]

arXiv:1606.09457PoS LL2016 (2016) 033by: Adams, Luise (U. Mainz, PRISMA) et al.Abstract: We summarize recent computations with a class of elliptic generalizations of polylogarithms, arising from the massive sunrise integral. For the case of arbitrary masses we obtain results in two and four space-time dimensions. The iterated integral structure of our functi […]

arXiv:1603.00420J.Phys.Conf.Ser. 762 (2016) 012067by: Bogner, Christian (Humboldt U., Berlin)Abstract: In this talk, we discuss recent progress in the application of generalizations of polylogarithms in the symbolic computation of multi-loop integrals. We briefly review the Maple program MPL which supports a certain approach for the computation of Feynman in […]

arXiv:1601.03646PoS RADCOR2015 (2016) 096by: Adams, Luise (Mainz U.) et al.Abstract: A walk on sunset boulevard can teach us about transcendental functions associated to Feynman diagrams. On this guided tour we will see multiple polylogarithms, differential equations and elliptic curves. A highlight of the tour will be the generalisation of the polylogarithm […]